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We very recently predicted the appearance of a Weyl Semimetal phase in TaAs. Now verified experimentally, this prediction realizes one more part of the wide range of exotic phenomena that appear in topological materials. I will present a general strategy to look for Weyl semimetals, including the likely symmetry groups of materials that make Weyl nodes likely. I will predict several other materials where Weyl nodes exist, as well as a new type of Weyl fermions that we predict exist in WTe2. Time permitting, I will discuss recent work on Majorana fermions in systems with spin-orbit coupling and new material where a three-dimensional doubled version of the Quantum Spin Hall state exists.